Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
594 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20244368 | C2 | semidirect |
| 5. #20241951 | C2 | semidirect |
| 6. #20241216 | C2 | semidirect |
| 7. C47×#1286 | C2 | semidirect |
| 11. #15689496 | C4 | semidirect |
| 12. #15689470 | C4 | semidirect |
| 32. #13094024 | C2×C4 | semidirect |
| 33. #13094024 | C2×C4 | semidirect |
| 64. C4×C8×C47 | C2×C4 | semidirect |
| 115. C4×Dic47 | SD16 | semidirect |
| 194. #1286 | D47 | semidirect |
| 221. C47 | #9295 | semidirect |
| 257. C4×C8 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254331 | 2 |
| #20246111 | 2 |
| #20244368 | 2 |
| #20242057 | 2 |
| #20241951 | 2 |
| #20241216 | 2 |
| C47×#1286 | 2 |
| #9295 | 47 |